Hemimage family: Difference between revisions

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 = Hemimage =
-[[Comma]]: hemimage 10976/10935
+Subgroup: 2.3.5.7
--limit minimax
+[[Comma list]]: 10976/10935
-[|1 0 0 0&gt;, |5/8 1/8 -1/8 3/8&gt;,
+[[Minimax tuning]]:
-|5/8 -7/8 7/8 3/8&gt;, |0 0 0 1&gt;]
+* [[7-odd-limit]]
+: [|1 0 0 0&gt;, |5/8 1/8 -1/8 3/8&gt;, |5/8 -7/8 7/8 3/8&gt;, |0 0 0 1&gt;]
+: [[Eigenmonzo]]s: 2, 8/7, 6/5
+* [[9-odd-limit]]
+: [|1 0 0 0&gt;, |5/9 2/9 -1/9 1/3&gt;, |10/9 -14/9 7/9 2/3&gt;, |0 0 0 1&gt;]
+: [[Eigenmonzo]]s: 2, 10/9, 8/7
-[[Eigenmonzo]]s: 2, 8/7, 6/5
+[[Mapping]]: [&lt;1 0 2 -1|, &lt;0 1 2 3|, &lt;0 0 -3 -1|]
--limit minimax
+Mapping generators: ~2, ~3, ~27/14
-[|1 0 0 0&gt;, |5/9 2/9 -1/9 1/3&gt;,
+{{Val list|legend=1| 14, 19, 41, 58, 77, 80, 99, 118, 140, 217, 316, 338, 357, 415, 456, 654, 695 }}
-|10/9 -14/9 7/9 2/3&gt;, |0 0 0 1&gt;]
-[[Eigenmonzo]]s: 2, 10/9, 8/7
+[[Badness]]: 0.199 × 10<sup>-3</sup>
-Map: [&lt;1 0 2 -1|, &lt;0 1 2 3|, &lt;0 0 -3 -1|]
-[[Generator]]s: 2, 3, 27/14
-[[EDO|Edos]]: 14, 19, 41, 58, 77, 80, [[99edo|99]], [[118edo|118]], [[140edo|140]], [[217edo|217]], [[316edo|316]], [[338edo|338]], [[357edo|357]], [[415edo|415]], [[456edo|456]], [[654edo|654]], [[695edo|695]]
-Badness: 0.000199
 [[Projection pair]]: 5 10976/2187 to 2.3.7
 = Uni =
-[[Comma]]s: 540/539, 896/891
+Subgroup: 2.3.5.7.11
-[[Minimax tuning]]
+[[Comma list]]: 540/539, 896/891
-[|1 0 0 0 0&gt;, |16/11 6/11 1/11 0 -3/11&gt;,
+Mapping: [&lt;1 0 2 -1 6|, &lt;0 1 2 3 -1|, &lt;0 0 -3 -1 -1|]
-|0 0 1 0 0&gt;, |19/11 14/11 6/11 0 -7/11&gt;,
-|32/11 -10/11 2/11 0 5/11&gt;]
-[[Eigenmonzo]]s: 2, 11/9, 5/4
+[[Minimax tuning]]:
+* [[11-odd-limit]]
+: [|1 0 0 0 0&gt;, |16/11 6/11 1/11 0 -3/11&gt;, |0 0 1 0 0&gt;, |19/11 14/11 6/11 0 -7/11&gt;, |32/11 -10/11 2/11 0 5/11&gt;]
+: [[Eigenmonzo]]s: 2, 11/9, 5/4
-Map: [&lt;1 0 2 -1 6|, &lt;0 1 2 3 -1|, &lt;0 0 -3 -1 -1|]
+{{Val list|legend=1| 19, 22, 41, 58, 80, 121 }}
-[[Generator]]s: 2, 3, 27/14
+Badness: 0.702 × 10<sup>-3</sup>
-[[EDO|Edos]]: [[19edo|19]], [[22edo|22]], [[41edo|41]], [[58edo|58]], [[80edo|80]], [[121edo|121]]
+== 13-limit ==
+Subgroup: 2.3.5.7.11.13
-Badness: 0.000702
+Comma list: 352/351, 364/363, 540/539
-== 13-limit ==
+Mapping: [&lt;1 0 2 -1 6 11|, &lt;0 1 2 3 -1 -4|, &lt;0 0 -3 -1 -1 -1|]
-Commas: 352/351, 364/363, 540/539
-Map: [&lt;1 0 2 -1 6 11|, &lt;0 1 2 3 -1 -4|, &lt;0 0 -3 -1 -1 -1|]
+Vals: {{Val list| 22, 41, 58, 80, 121 }}
-EDOs: 22, 41, 58, 80, 121
+Badness: 1.06 × 10<sup>-3</sup>
-Badness: 0.00106
+== Tin ==
+Subgroup: 2.3.5.7.11.13
-== Tin ==
+Comma list: 144/143, 196/195, 729/728
-Commas: 144/143, 196/195, 729/728
-Map: [&lt;1 0 2 -1 6 -2|, &lt;0 1 2 3 -1 3|, &lt;0 0 -3 -1 -1 1|]
+Mapping: [&lt;1 0 2 -1 6 -2|, &lt;0 1 2 3 -1 3|, &lt;0 0 -3 -1 -1 1|]
-EDOs: 19, 36, 41, 58
+Vals: {{Val list| 19, 36, 41, 58 }}
-Badness: 0.00107
+Badness: 1.07 × 10<sup>-3</sup>
 = Turan =
-[[Comma]]s: 441/440, 10976/10935
+Subgroup: 2.3.5.7.11
-[[Minimax tuning]]
-[|1 0 0 0 0&gt;, |19/12 -2/3 1/12 0 1/4&gt;,
-|19/6 -10/3 7/6 0 1/2&gt;,
-|37/12 -8/3 7/12 0 3/4&gt;,
-|19/6 -10/3 1/6 0 3/2&gt;]
-[[Eigenmonzo]]s: 2, 10/9, 11/9
+[[Comma list]]: 441/440, 10976/10935
-Map: [&lt;1 0 2 -1 -7|, &lt;0 1 2 3 6|, &lt;0 0 -3 -1 1|]
+[[Mapping]]: [&lt;1 0 2 -1 -7|, &lt;0 1 2 3 6|, &lt;0 0 -3 -1 1|]
-[[Generator]]s: 2, 3, 27/14
+[[Minimax tuning]]:
+: [|1 0 0 0 0&gt;, |19/12 -2/3 1/12 0 1/4&gt;, |19/6 -10/3 7/6 0 1/2&gt;, |37/12 -8/3 7/12 0 3/4&gt;, |19/6 -10/3 1/6 0 3/2&gt;]
+: [[Eigenmonzo]]s: 2, 10/9, 11/9
-[[EDO|Edos]]: [[41edo|41]], [[58edo|58]], [[118edo|118]], [[159edo|159]], [[217edo|217]], [[335edo|335]]
+{{Val list|legend=1| 41, 58, 118], 159, 217, 335 }}
-Badness: 0.000936
+[[Badness]]: 0.936 × 10<sup>-3</sup>
-[[Category:Theory]]
+[[Category:Regular temperament theory]]
 [[Category:Temperament family]]
 [[Category:Hemimage]]
 [[Category:Rank 3]]